the difference between two numbers is 7. the larger number is 9 less than 3 times the smaller. find the numbers
To solve this problem, we can set up a system of equations. Let's assign variables to the two numbers.
Let x be the smaller number.
Let y be the larger number.
We are given two pieces of information:
1. "The difference between two numbers is 7" can be expressed as: y - x = 7.
2. "The larger number is 9 less than 3 times the smaller" can be expressed as: y = 3x - 9.
Now we have a system of equations:
y - x = 7
y = 3x - 9
To find the values of x and y, we can use the method of substitution or elimination.
Let's solve this system using substitution:
Substitute the value of y from the second equation into the first equation:
(3x - 9) - x = 7
3x - 9 - x = 7
2x - 9 = 7
2x = 7 + 9
2x = 16
x = 16/2
x = 8
Now, substitute the value of x back into the second equation to find y:
y = 3(8) - 9
y = 24 - 9
y = 15
So, the smaller number is 8, and the larger number is 15.
Let a = smaller and b = larger number.
a = b - 7
3a - 9 = b
Substitute b-7 for a in the second equation and solve for b. Put that value in the first equation to find a. To Check, put both values into the second equation.